Faraday-waves contact-line shear gradient induces streaming flow and tracers' self-organization: from rotating rings to spiral galaxy-like patterns

TL;DR

This study demonstrates how Faraday wave-induced shear gradients at the contact line generate streaming flows that self-organize tracers into various patterns, including rings and spiral-like structures, through experimental and modeling approaches.

Contribution

The paper introduces a new understanding of how Faraday wave-induced shear gradients drive tracer self-organization, supported by experimental observations and a minimal 2D model.

Findings

Streaming currents form in cells dictated by wave symmetry.

Tracer patterns depend on wave amplitude, from dispersed to spiral structures.

Shear at the contact line is the main source of streaming flow.

Abstract

In this letter we experimentally demonstrate self-organization of small tracers under the action of longitudinal Faraday waves in a narrow container. We observe a steady current formation dividing the interface in small cells given by the symmetries of the Faraday wave. These streaming currents are rotating in each cell and their circulation increases with wave amplitude. This streaming flow drives the tracers to form patterns, whose shapes depend on the Faraday wave's amplitude: from low to high amplitudes we find dispersed tracers, a narrow rotating ring and a spiral galaxy-like pattern. We first describe the main pattern features, and characterize the wave and tracers' motion. We then show experimentally that the main source of the streaming flow comes from the time and spatial dependent shear at the wall contact line, created by the Faraday wave itself. We end by presenting a 2D model that considers the minimal ingredients present in the Faraday experiment, namely the stationary circulation, the stretching component due to the oscillatory wave and a steady converging field, which combined produce the observed self-organized patterns.